Corresponding relationships between nodes of decomposition tree of wavelet packet and frequency bands of signal subspace

Mallat decomposition algorithm of wavelet packet transform can divide broader band into narrower ones with equal bandwidth and no overlapping each other. However, order by size of frequency within signal subspace is not in accordance with that of node label of decomposition tree. Therefore, it is not easy to determine frequency range of reconstructed signal from each node. In this paper, by analyzing the relationship between Mallat decomposition algorithm of wavelet packet transform and decomposition filter and setting operation rule of binary conversion of band labels into node labels, we find the corresponding relationships between nodes of decomposition tree and frequency bands of signal subspace. Then, the conclusion is verified by analog signals. Also, it shows that the arranged rule of bands of signal subspace summarized in the paper is correct.